Question 565: Centre of Mass and Rotational Motion

Question

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is $\frac{\mathrm{Ma}^2}{6}$, where '$M$' is the mass and '$a$' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Accepted Answer

$\begin{aligned}
\mathrm{I}_{\mathrm{O}} & =\frac{\mathrm{Ma}^2}{6} \
\mathrm{AB} & =\sqrt{2 \mathrm{a}^2}=\sqrt{2} \mathrm{a} \
	herefore \quad \mathrm{AO} & =\frac{\mathrm{a}}{\sqrt{2}}=\mathrm{h} \
	herefore \quad \mathrm{I}_{\mathrm{A}} & =\mathrm{I}_0+\mathrm{Mh}^2 \
& =\frac{\mathrm{Ma}^2}{6}+\frac{\mathrm{Ma}^2}{2} \
& =\frac{8 \mathrm{Ma}^2}{12}=\frac{2}{3} \mathrm{Ma}^2
\end{aligned}$

Answer

$\frac{\mathrm{Ma}^2}{6}$

Answer

$\frac{2 \mathrm{Ma}^2}{3}$

Answer

$\frac{\mathrm{Ma}^2}{3}$

Answer

$\frac{2 \mathrm{Ma}^2}{5}$

Centre of Mass and Rotational Motion

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